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Multiple dispatch solves the expression problem so intuitively and straightforwardly that it's often hard to remember why it was a problem in the first place. I

Multiple dispatch solves the expression problem so intuitively and straightforwardly that it's often hard to remember why it was a problem in the first place. In Julia, for example: abstract Exp immutable Lit <: Exp value::Int end immutable Add <: Exp left::Exp right::Exp end evaluate(lit::Lit) = lit.value evaluate(add::Add) = evaluate(add.left) + evaluate(add.right) If you want to add a new operation, it's straightforward: view(lit::Lit) = string(lit.value) view(add::Add) = string("(", view(add.left), " + ", view(add.right), ")") If you want to add a new type of expression, it's also straightforward: immutable Mul <: Exp left::Exp right::Exp end evaluate(mul::Mul) = evaluate(mul.left) * evaluate(mul.right) view(mul::Mul) = string("(", view(mul.left), " * ", view(mul.right), ")") That's all there is to it. Of course, it's actually the external dispatch that's crucial, not the multiple dispatch. (But multiple part is very handy for other things, especially in numerical work).

scscsc 12y ago
If you forget to write view for the Mul case, does the compiler issue an error? (in other words, is it strongly typed?)
danking00 12y ago
This seems like a likewise elegant solution. However, it's not immediately obvious to me how to make this work with a static type discipline. Are there languages that do this? It seems like part of the benefits of the approaches described in the blog post is that the type system will catch incomplete extensions to the existing data or methods.
- beagle3 12y ago
  Nim Lang (previously Nimrod) can do that, if I understand correctly.
- yummyfajitas 12y ago
  In Scala, for algebraic data types like expressions and addition, you'd just use pattern matching. That would encompass the example fully. Scala has an "external" dispatch mechanism as well, basically a way to create new typed methods, namely pimping: implicit class FooWrapper(foo: Foo) extends AnyVal { def newMethod: Int = ... } val x: Foo = new Foo() x.newMethod These are all checked at compile time. Note that the example given above is actually not multiple dispatch, but merely adding methods to a type. It differs from function overloading (a Java/C++) feature only syntactically. Multiple dispatch would be dispatch on multiple type arguments, not simply one (which Julia has, but Scala does not).
  - seanmcdirmid 12y ago
    As does C# with extension methods. It is especially useful when you have a generic class: class Foo<X> { ... } static class Foos { static void DoFooInt(this Foo<int> self) { .... } } new Foo<int>().DoFooInt(); I built a whole pimped library called "Bling" for C#/WPF to lift values into signal form around this technique. http://bling.codeplex.com http://bling.codeplex.com Unfortunately, operators can't be externally extended in C#, so there is still a lot of wrapper creation, but extension methods can be used for that; e.g. Signal<int> a = ..., b = ...; var c = a.Bl() + b.Bl(); Bl is an extension method for signal ints that returns a wrapper around the argument that allows for access to the + method. Bl is overloaded for a variety of types to provide access to those wrappers.
ddandd 12y ago
I believe that a similar approach can also be used in C++ with the help of ADL [1] and some template magic. Though it may only work on expressions whose concrete type may be known at compile-time (which makes it pretty useless). [1] http://en.wikipedia.org/wiki/Argument-dependent_name_lookup http://en.wikipedia.org/wiki/Argument-dependent_name_lookup
gclaramunt 12y ago
Hmm, but when you add a new type of expression, you still have to write the particular implementation of the functions for that type. There are other approaches to generic programming where when you add a new datatype, all the already defined functions work, and if you add a new function, it automatically works for all the datatypes.
- StefanKarpinski 12y ago
  I started to write those but it got a bit long for a comment. – Fermat
  - gclaramunt 12y ago
    But those are pretty short to write (explaining the category theory machinery behind it takes several book chapters tho :) )
sclv 12y ago
It is well known that in the untyped (or dynamically typed if you prefer that language) case then the expression problem trivializes. In fact, if we sacrifice type-safety then the problem trivializes in a typed language too.

scscsc 12y ago

If you forget to write view for the Mul case, does the compiler issue an error? (in other words, is it strongly typed?)

danking00 12y ago

This seems like a likewise elegant solution. However, it's not immediately obvious to me how to make this work with a static type discipline. Are there languages that do this? It seems like part of the benefits of the approaches described in the blog post is that the type system will catch incomplete extensions to the existing data or methods.

beagle3 12y ago
Nim Lang (previously Nimrod) can do that, if I understand correctly.
yummyfajitas 12y ago
In Scala, for algebraic data types like expressions and addition, you'd just use pattern matching. That would encompass the example fully. Scala has an "external" dispatch mechanism as well, basically a way to create new typed methods, namely pimping: implicit class FooWrapper(foo: Foo) extends AnyVal { def newMethod: Int = ... } val x: Foo = new Foo() x.newMethod These are all checked at compile time. Note that the example given above is actually not multiple dispatch, but merely adding methods to a type. It differs from function overloading (a Java/C++) feature only syntactically. Multiple dispatch would be dispatch on multiple type arguments, not simply one (which Julia has, but Scala does not).
- seanmcdirmid 12y ago
  As does C# with extension methods. It is especially useful when you have a generic class: class Foo<X> { ... } static class Foos { static void DoFooInt(this Foo<int> self) { .... } } new Foo<int>().DoFooInt(); I built a whole pimped library called "Bling" for C#/WPF to lift values into signal form around this technique. http://bling.codeplex.com http://bling.codeplex.com Unfortunately, operators can't be externally extended in C#, so there is still a lot of wrapper creation, but extension methods can be used for that; e.g. Signal<int> a = ..., b = ...; var c = a.Bl() + b.Bl(); Bl is an extension method for signal ints that returns a wrapper around the argument that allows for access to the + method. Bl is overloaded for a variety of types to provide access to those wrappers.

ddandd 12y ago

I believe that a similar approach can also be used in C++ with the help of ADL [1] and some template magic. Though it may only work on expressions whose concrete type may be known at compile-time (which makes it pretty useless). [1] http://en.wikipedia.org/wiki/Argument-dependent_name_lookup http://en.wikipedia.org/wiki/Argument-dependent_name_lookup

gclaramunt 12y ago

Hmm, but when you add a new type of expression, you still have to write the particular implementation of the functions for that type. There are other approaches to generic programming where when you add a new datatype, all the already defined functions work, and if you add a new function, it automatically works for all the datatypes.

StefanKarpinski 12y ago
I started to write those but it got a bit long for a comment. – Fermat
- gclaramunt 12y ago
  But those are pretty short to write (explaining the category theory machinery behind it takes several book chapters tho :) )

sclv 12y ago

It is well known that in the untyped (or dynamically typed if you prefer that language) case then the expression problem trivializes. In fact, if we sacrifice type-safety then the problem trivializes in a typed language too.